Eventually, to save money, the WTBTS decided to have everyone BYO food (making like the decision was to benefit the people). They also tied to this the "rule": Do not go to public vendors and buy your lunch. Bring your own! Me thinks this was because, if you spend money on food, you will donate less to the Society.
When WTS stopped "selling" food because it might be considered a profit that was taxable to the government, they hoped the members would donate enough money to still keep offering the food (which was a huge cash cow for them). Well, the members did not. So food was done away with.
The reason they insisted so heavily that people bring their own food was that many stadiums/auditoriums had kitchens and venders and wanted to open these during the JW events, but Watchtower said "Our people would not use your venders, they are there to be among their brothers and sisters and would rather bring their own." Really, it was as you say- money going to the vender would not make it into the box. Could you imagine the pizza, hot dog, beer, venders being open during an assembly?
By the time I was fully awake, I attended one District Assembly still as an elder and barely paid attention to anything said but kept busy as an attendant. I couldn't imagine sitting there for even a public talk now, without laughing out loud at the logic flaws and comedy of misunderstood conceptions.